Abstract
The problem of calculating the radiation of sound from an unflanged circular waveguide is a classical acoustical problem, which received considerable discussion in Rayleigh's treatise on the theory of sound. However, the exact solution of this problem was obtained only two decades ago by Levine, Schwinger, and Carrier for a plane wave and by Vajnshtejn for the higher modes. Owing to the complexity of the formulas obtained, numerical results have been very limited. Using modern high-speed computers, the authors bare greatly extended the previous calculations so that the theory is now useful in problems involving high-frequency sound sources operating within waveguides with flow. The proposed paper will review the exact solution for the unflanged circular waveguide and present a generalization of Vajnshtejn's results that includes flow. The effects of mode number, source frequency, and flow Mach number on reflection coefficients, radiated power, and directivity patterns will be discussed. Comparisons are made with several approximate methods now in use and the range of validity of these methods indicated.
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